In the author's previous articles on the pendulum with oscillating suspension, a clear physical explanation of the phenomenon of dynamic stabilization of the inverted pendulum [1] is given and the genetic relationship of parametric subharmonic resonances with the conditions of dynamic stabilization [2]. In this article, on the basis of this connection, the updated values of the lower and upper limits of dynamic stabilization are obtained, which are fair in the wider area of the system parameters. In particular, the obtained stability limits are valid at relatively low pendulum suspension oscillation frequencies, when the method of separation of fast and slow movements does not work, and the traditional criterion of stability of the inverted pendulum is not applicable. The results of computer simulations confirming the extended criterion of stability. are given.